Modeling of nonlinear dynamic systems

Dynamic nonlinear systems can be modeled with the aid of nonlinear differential equations. The solution of these equations can almost always only be found through numerical methods. In this section, we will give some parameters that describe dynamic nonlinear effects. Aside from these parameters, the following parameters from the previous paragraph also apply to dynamic nonlinear systems:

1. Differential gain

   In dynamic nonlinear systems, the differential gain depends on frequency. Since the small-signal gain in dynamic systems is complex, the differential gain is also complex with both magnitude and phase (differential gain and differential phase).

2. THD

   In dynamic nonlinear systems, the harmonic distortion becomes a function of the frequency and the relations between the differential gain and the second and third order harmonic distortions are no longer valid.

3. Intermodulation

   In dynamic nonlinear systems, the intermodulation distortion becomes a function of the frequency and the relations between the differential gain and the second and third order intermodulation distortions are no longer valid.

4. Gain compression

   In dynamic nonlinear systems the 1dB compression point becomes a function of the frequency and the relation between the IP3 and the 1dB compression point is no longer valid.

5. Slew rate

   The limitation of the maximum rate of change of the output signal is called the slew rate limitation. Let \(y(t)\) be the system response to an input signal. The positive slew rate \(SR^{+}\) is defined as

   \[SR^{+}=\left. \frac{dy(t)}{dt}\right\vert _{\max};\text{where }\frac{dy(t)}{dt}\geq0.\]

   The negative slew rate \(SR^{-}\) is defined as

\[SR^{-}=-\left\vert \frac{dy(t)}{dt}\right\vert _{\max};\text{ where } \frac{dy(t)}{dt}<0.\]